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Title: Importance sampling as a variational approximation
Authors: Nott, D.J. 
Li, J. 
Fielding, M. 
Keywords: Bayesian computation
Importance sampling
Variational approximation
Issue Date: Aug-2011
Citation: Nott, D.J., Li, J., Fielding, M. (2011-08). Importance sampling as a variational approximation. Statistics and Probability Letters 81 (8) : 1052-1055. ScholarBank@NUS Repository.
Abstract: There is a well-recognized need to develop Bayesian computational methodologies that scale well to large data sets. Recent attempts to develop such methodology have often focused on two approaches-variational approximation and advanced importance sampling methods. This note shows how importance sampling can be viewed as a variational approximation, achieving a pleasing conceptual unification of the two points of view. We consider a particle representation of a distribution as defining a certain parametric model and show how the optimal approximation (in the sense of minimization of a Kullback-Leibler divergence) leads to importance sampling type rules. This new way of looking at importance sampling has the potential to generate new algorithms by the consideration of deterministic choices of particles in particle representations of distributions. © 2011 Elsevier B.V.
Source Title: Statistics and Probability Letters
ISSN: 01677152
DOI: 10.1016/j.spl.2011.02.028
Appears in Collections:Staff Publications

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